Write each of the following functions in the form $w\ =\ u(x,y)\ +\ iv(x,y)$ :

(1) $f(z)\ =\ 2 z^2\ +\ 4 z\ +\ 2 i\ +\ 4$

$+\ i$

(2) $h(z)\ =\ \frac{5 z\ +\ 4 i}{2 z^2\ +\ 4}$

$+\ i$

(3) $F(z)\ =\ e^{3 z}$

$+\ i$